Results 11 to 20 of about 176 (118)
Methods of constructing hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1985 In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we give a negative answer to the question of whether every hyperfield is isomorphic to a quotient KG of a field K by some subgroup G of its multiplicative ...
Ch. G. Massouros
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A class of hyperrings and hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1983 Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H.
Marc Krasner
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Characteristic, C-Characteristic and Positive Cones in Hyperfields
Mathematics, 2023 We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields.
Dawid Edmund Kedzierski +2 more
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Recent results in hyperring and hyperfield theory [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the sum of two elements is a subset of the structure.
Anastase Nakassis
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Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices.
Atamewoue Surdive +3 more
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Tropical geometry over the tropical hyperfield [PDF]
Rocky Mountain Journal of Mathematics, 2022 In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a nonarchimedean absolute value can be considered as a morphism into the tropical hyperfield.
Oliver Lorscheid
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On the Borderline of Fields and Hyperfields
Mathematics, 2023 The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is related ...
Christos G. Massouros +1 more
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Valuations on Structures More General Than Fields
Computer Sciences & Mathematics Forum, 2023 Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some ...
Alessandro Linzi
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Commutative hypergroups associated with a hyperfield [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2017 Let [Formula: see text] be a commutative hypergroup and [Formula: see text] a discrete commutative hypergroup. In this paper we introduce a commutative hypergroup [Formula: see text] associated with a hyperfield [Formula: see text] of [Formula: see text] based on [Formula: see text].
Heyer, Herbert +3 more
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